Problem: Simplify the following expression: $ a = \dfrac{-7t + 4}{-2t} + \dfrac{-5}{6} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-7t + 4}{-2t} \times \dfrac{6}{6} = \dfrac{-42t + 24}{-12t} $ Multiply the second expression by $\dfrac{-2t}{-2t}$ $ \dfrac{-5}{6} \times \dfrac{-2t}{-2t} = \dfrac{10t}{-12t} $ Therefore $ a = \dfrac{-42t + 24}{-12t} + \dfrac{10t}{-12t} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-42t + 24 + 10t}{-12t} $ $a = \dfrac{-32t + 24}{-12t}$ Simplify the expression by dividing the numerator and denominator by -4: $a = \dfrac{8t - 6}{3t}$